Annual bone grafting surgeries due to bone fractures, resections of affected bones, skeletal anomalies, osteoporosis, etc. exceed two million worldwide. In this regard, the creation of new materials for bone tissue repair is one of the urgent tasks of modern medicine. Additive manufacturing, or 3D printing, offers great opportunities for the development of materials with diverse properties and designs. In this study, the one-pot technique for the production of 3D scaffolds based on poly(ε-caprolactone) (PCL) loaded with an antibiotic or anti-inflammatory drug was proposed. In contrast to previously described methods to prepare drug-containing scaffolds, drug-loaded PCL scaffolds were prepared by direct 3D printing from a polymer/drug blend. An investigation of the mechanical properties of 3D-printed scaffolds containing 0.5–5 wt% ciprofloxacin (CIP) or dexamethasone (DEX) showed almost no effect of the drug (compression modulus ~70–90 MPa) compared to unfilled PCL (74 MPa). At the same time, introducing the drug and increasing its content in the PCL matrix contributed to a 1.8–6.8-fold decrease in the specific surface area of the scaffold, depending on composition. The release of CIP and DEX in phosphate buffer solution and in the same buffer containing lipase revealed a faster release in enzyme-containing medium within 45 days. Furthermore, drug release was more intensive from scaffolds with a low drug load. Analysis of the release profiles using a number of mathematical dissolution models led to the conclusion that diffusion dominates over other probable factors. In vitro biological evaluation of the scaffolds containing DEX showed moderate toxicity against osteoblast-like and leukemia monocytic cells. Being 3D-printed together with PCL both drugs retain their biological activity. PCL/CIP and PCL/DEX scaffolds demonstrated antibacterial properties against Pseudomonas aeruginosa (a total inhibition after 48 h) and anti-inflammatory activity in experiments on TNFα-activated monocyte cells (a 4-time reduction in CD-54 expression relative to control), respectively.